Abstract

Recently it was shown that the incoherent part of light scattered from random surfaces with even profiles displays a well-defined peak in the specular direction. This effect has been termed specular enhancement.

Here we present an experimental and theoretical study of the scattering of two coherent optical beams from a symmetric random surface. It is found that, in addition to the two sharp peaks corresponding to the enhancements in the specular directions, there is a third peak that is due to the interaction of the two optical beams at the surface.

© 1992 Optical Society of America

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References

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  1. M. Nieto-Vesperinas, J. M. Soto-Crespo, “Light-diffracted intensities from very deep gratings,” Phys. Rev. B 38, 7250 (1988).
    [CrossRef]
  2. M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1989).
    [CrossRef]
  3. E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Light scattering from one-dimensional surfaces with an even profile,” in Optical Space Communication, G. Otrio, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1131, 18–29 (1990).
  4. E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. H. Gu, “Coherent effects in the scattering of light from random surfaces with symmetries,” Opt. Lett. 16, 123–125 (1991).
    [CrossRef]
  5. Z.-H. Gu, A. A. Maradudin, E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Enhanced transmission through randomly rough surfaces,” Waves Random Med. 1, S75–S90 (1991).
    [CrossRef]
  6. A. A. Maradudin, J. Q. Lu, T. Michel, Z.-H. Gu, J. C. Dainty, A. J. Sant, E. R. Méndez, M. Nieto-Vesperinas, “Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films,” Waves Random Med. 1, S129–S141 (1991).
    [CrossRef]
  7. A. R. McGurn, A. A. Maradudin, “Localization effects in the elastic scattering of light from a randomly rough surface,” J. Opt. Soc. Am. B 4, 910–926 (1987).
    [CrossRef]
  8. A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
    [CrossRef]
  9. K. A. O’Donnell, E. R. Méndez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
    [CrossRef]
  10. M.-J. Kim, J. C. Dainty, A. T. Friberg, A. J. Sant, “Experimental study of enhanced backscattering from one-and two-dimensional random rough surfaces,” J. Opt. Soc. Am. A 7, 569–577 (1990).
    [CrossRef]
  11. Z. H. Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, “Experimental Study of the opposition effect in the scattering of light from a randomly rough metal surface,” Appl. Opt. 28, 537–543 (1989).
    [CrossRef] [PubMed]
  12. J. M. Soto-Crespo, M. Nieto-Vesperinas, “Electromagnetic scattering from very rough random surfaces and deep reflection gratings,” J. Opt. Soc. Am. A 6, 367–384 (1989).
    [CrossRef]
  13. A. R. McGurn, A. A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–281 (1989).
    [CrossRef]
  14. Z. H. Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, E. R. Méndez, “Enhanced transmission through rough metal surfaces,” Appl. Opt. 30, 4094–4102 (1991).
    [CrossRef] [PubMed]
  15. E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. H. Gu, “Photofabrication of one-dimensional rough surfaces for light scattering experiments,” Appl. Opt. 30, 4103–4112 (1991).
    [CrossRef] [PubMed]
  16. W. T. Welford, “Optical estimation of statistics of surface roughness from light scattering measurements,” Opt. Quantum Electron. 9, 269–287 (1977).
    [CrossRef]
  17. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 84.
  18. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 82.
  19. A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. of Phys. 203, 255–307 (1990).
    [CrossRef]
  20. A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of P-polarized light from a large amplitude random metallic grating,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North Holland, Amsterdam, 1990), pp. 157–174.
  21. A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large amplitude random metallic grating,” Opt. Lett. 14, 151–153 (1989).
    [CrossRef] [PubMed]
  22. V. Celli, P. Tran, A. A. Maradudin, J. Lu, T. Michel, Z. H. Gu, “Waves on corrugated surfaces: K-gaps and enhanced backscattering,” in Laser Optics of Condensed Matter, E. Garmire, A. A. Maradudin, K. K. Rebane, eds. (Plenum, New York, 1991), Vol. 2, pp. 315–323.
    [CrossRef]

1991

Z.-H. Gu, A. A. Maradudin, E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Enhanced transmission through randomly rough surfaces,” Waves Random Med. 1, S75–S90 (1991).
[CrossRef]

A. A. Maradudin, J. Q. Lu, T. Michel, Z.-H. Gu, J. C. Dainty, A. J. Sant, E. R. Méndez, M. Nieto-Vesperinas, “Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films,” Waves Random Med. 1, S129–S141 (1991).
[CrossRef]

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. H. Gu, “Coherent effects in the scattering of light from random surfaces with symmetries,” Opt. Lett. 16, 123–125 (1991).
[CrossRef]

Z. H. Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, E. R. Méndez, “Enhanced transmission through rough metal surfaces,” Appl. Opt. 30, 4094–4102 (1991).
[CrossRef] [PubMed]

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. H. Gu, “Photofabrication of one-dimensional rough surfaces for light scattering experiments,” Appl. Opt. 30, 4103–4112 (1991).
[CrossRef] [PubMed]

1990

M.-J. Kim, J. C. Dainty, A. T. Friberg, A. J. Sant, “Experimental study of enhanced backscattering from one-and two-dimensional random rough surfaces,” J. Opt. Soc. Am. A 7, 569–577 (1990).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. of Phys. 203, 255–307 (1990).
[CrossRef]

1989

1988

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Light-diffracted intensities from very deep gratings,” Phys. Rev. B 38, 7250 (1988).
[CrossRef]

1987

1985

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

1977

W. T. Welford, “Optical estimation of statistics of surface roughness from light scattering measurements,” Opt. Quantum Electron. 9, 269–287 (1977).
[CrossRef]

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 84.

Celli, V.

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

V. Celli, P. Tran, A. A. Maradudin, J. Lu, T. Michel, Z. H. Gu, “Waves on corrugated surfaces: K-gaps and enhanced backscattering,” in Laser Optics of Condensed Matter, E. Garmire, A. A. Maradudin, K. K. Rebane, eds. (Plenum, New York, 1991), Vol. 2, pp. 315–323.
[CrossRef]

Dainty, J. C.

A. A. Maradudin, J. Q. Lu, T. Michel, Z.-H. Gu, J. C. Dainty, A. J. Sant, E. R. Méndez, M. Nieto-Vesperinas, “Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films,” Waves Random Med. 1, S129–S141 (1991).
[CrossRef]

M.-J. Kim, J. C. Dainty, A. T. Friberg, A. J. Sant, “Experimental study of enhanced backscattering from one-and two-dimensional random rough surfaces,” J. Opt. Soc. Am. A 7, 569–577 (1990).
[CrossRef]

Dummer, R. S.

Friberg, A. T.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 82.

Gu, Z. H.

Gu, Z.-H.

Z.-H. Gu, A. A. Maradudin, E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Enhanced transmission through randomly rough surfaces,” Waves Random Med. 1, S75–S90 (1991).
[CrossRef]

A. A. Maradudin, J. Q. Lu, T. Michel, Z.-H. Gu, J. C. Dainty, A. J. Sant, E. R. Méndez, M. Nieto-Vesperinas, “Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films,” Waves Random Med. 1, S129–S141 (1991).
[CrossRef]

Kim, M.-J.

Lu, J.

V. Celli, P. Tran, A. A. Maradudin, J. Lu, T. Michel, Z. H. Gu, “Waves on corrugated surfaces: K-gaps and enhanced backscattering,” in Laser Optics of Condensed Matter, E. Garmire, A. A. Maradudin, K. K. Rebane, eds. (Plenum, New York, 1991), Vol. 2, pp. 315–323.
[CrossRef]

Lu, J. Q.

A. A. Maradudin, J. Q. Lu, T. Michel, Z.-H. Gu, J. C. Dainty, A. J. Sant, E. R. Méndez, M. Nieto-Vesperinas, “Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films,” Waves Random Med. 1, S129–S141 (1991).
[CrossRef]

Maradudin, A. A.

A. A. Maradudin, J. Q. Lu, T. Michel, Z.-H. Gu, J. C. Dainty, A. J. Sant, E. R. Méndez, M. Nieto-Vesperinas, “Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films,” Waves Random Med. 1, S129–S141 (1991).
[CrossRef]

Z. H. Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, E. R. Méndez, “Enhanced transmission through rough metal surfaces,” Appl. Opt. 30, 4094–4102 (1991).
[CrossRef] [PubMed]

Z.-H. Gu, A. A. Maradudin, E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Enhanced transmission through randomly rough surfaces,” Waves Random Med. 1, S75–S90 (1991).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. of Phys. 203, 255–307 (1990).
[CrossRef]

A. R. McGurn, A. A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–281 (1989).
[CrossRef]

Z. H. Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, “Experimental Study of the opposition effect in the scattering of light from a randomly rough metal surface,” Appl. Opt. 28, 537–543 (1989).
[CrossRef] [PubMed]

A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large amplitude random metallic grating,” Opt. Lett. 14, 151–153 (1989).
[CrossRef] [PubMed]

A. R. McGurn, A. A. Maradudin, “Localization effects in the elastic scattering of light from a randomly rough surface,” J. Opt. Soc. Am. B 4, 910–926 (1987).
[CrossRef]

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

V. Celli, P. Tran, A. A. Maradudin, J. Lu, T. Michel, Z. H. Gu, “Waves on corrugated surfaces: K-gaps and enhanced backscattering,” in Laser Optics of Condensed Matter, E. Garmire, A. A. Maradudin, K. K. Rebane, eds. (Plenum, New York, 1991), Vol. 2, pp. 315–323.
[CrossRef]

A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of P-polarized light from a large amplitude random metallic grating,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North Holland, Amsterdam, 1990), pp. 157–174.

McGurn, A. R.

Z. H. Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, E. R. Méndez, “Enhanced transmission through rough metal surfaces,” Appl. Opt. 30, 4094–4102 (1991).
[CrossRef] [PubMed]

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. of Phys. 203, 255–307 (1990).
[CrossRef]

Z. H. Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, “Experimental Study of the opposition effect in the scattering of light from a randomly rough metal surface,” Appl. Opt. 28, 537–543 (1989).
[CrossRef] [PubMed]

A. R. McGurn, A. A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–281 (1989).
[CrossRef]

A. R. McGurn, A. A. Maradudin, “Localization effects in the elastic scattering of light from a randomly rough surface,” J. Opt. Soc. Am. B 4, 910–926 (1987).
[CrossRef]

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

Méndez, E. R.

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. H. Gu, “Coherent effects in the scattering of light from random surfaces with symmetries,” Opt. Lett. 16, 123–125 (1991).
[CrossRef]

A. A. Maradudin, J. Q. Lu, T. Michel, Z.-H. Gu, J. C. Dainty, A. J. Sant, E. R. Méndez, M. Nieto-Vesperinas, “Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films,” Waves Random Med. 1, S129–S141 (1991).
[CrossRef]

Z. H. Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, E. R. Méndez, “Enhanced transmission through rough metal surfaces,” Appl. Opt. 30, 4094–4102 (1991).
[CrossRef] [PubMed]

Z.-H. Gu, A. A. Maradudin, E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Enhanced transmission through randomly rough surfaces,” Waves Random Med. 1, S75–S90 (1991).
[CrossRef]

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. H. Gu, “Photofabrication of one-dimensional rough surfaces for light scattering experiments,” Appl. Opt. 30, 4103–4112 (1991).
[CrossRef] [PubMed]

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. of Phys. 203, 255–307 (1990).
[CrossRef]

A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large amplitude random metallic grating,” Opt. Lett. 14, 151–153 (1989).
[CrossRef] [PubMed]

K. A. O’Donnell, E. R. Méndez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
[CrossRef]

A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of P-polarized light from a large amplitude random metallic grating,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North Holland, Amsterdam, 1990), pp. 157–174.

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Light scattering from one-dimensional surfaces with an even profile,” in Optical Space Communication, G. Otrio, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1131, 18–29 (1990).

Michel, T.

A. A. Maradudin, J. Q. Lu, T. Michel, Z.-H. Gu, J. C. Dainty, A. J. Sant, E. R. Méndez, M. Nieto-Vesperinas, “Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films,” Waves Random Med. 1, S129–S141 (1991).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. of Phys. 203, 255–307 (1990).
[CrossRef]

A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large amplitude random metallic grating,” Opt. Lett. 14, 151–153 (1989).
[CrossRef] [PubMed]

A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of P-polarized light from a large amplitude random metallic grating,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North Holland, Amsterdam, 1990), pp. 157–174.

V. Celli, P. Tran, A. A. Maradudin, J. Lu, T. Michel, Z. H. Gu, “Waves on corrugated surfaces: K-gaps and enhanced backscattering,” in Laser Optics of Condensed Matter, E. Garmire, A. A. Maradudin, K. K. Rebane, eds. (Plenum, New York, 1991), Vol. 2, pp. 315–323.
[CrossRef]

Nieto-Vesperinas, M.

A. A. Maradudin, J. Q. Lu, T. Michel, Z.-H. Gu, J. C. Dainty, A. J. Sant, E. R. Méndez, M. Nieto-Vesperinas, “Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films,” Waves Random Med. 1, S129–S141 (1991).
[CrossRef]

J. M. Soto-Crespo, M. Nieto-Vesperinas, “Electromagnetic scattering from very rough random surfaces and deep reflection gratings,” J. Opt. Soc. Am. A 6, 367–384 (1989).
[CrossRef]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1989).
[CrossRef]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Light-diffracted intensities from very deep gratings,” Phys. Rev. B 38, 7250 (1988).
[CrossRef]

O’Donnell, K. A.

Ponce, M. A.

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. H. Gu, “Photofabrication of one-dimensional rough surfaces for light scattering experiments,” Appl. Opt. 30, 4103–4112 (1991).
[CrossRef] [PubMed]

Z.-H. Gu, A. A. Maradudin, E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Enhanced transmission through randomly rough surfaces,” Waves Random Med. 1, S75–S90 (1991).
[CrossRef]

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. H. Gu, “Coherent effects in the scattering of light from random surfaces with symmetries,” Opt. Lett. 16, 123–125 (1991).
[CrossRef]

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Light scattering from one-dimensional surfaces with an even profile,” in Optical Space Communication, G. Otrio, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1131, 18–29 (1990).

Ruiz-Cortés, V.

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. H. Gu, “Coherent effects in the scattering of light from random surfaces with symmetries,” Opt. Lett. 16, 123–125 (1991).
[CrossRef]

Z.-H. Gu, A. A. Maradudin, E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Enhanced transmission through randomly rough surfaces,” Waves Random Med. 1, S75–S90 (1991).
[CrossRef]

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. H. Gu, “Photofabrication of one-dimensional rough surfaces for light scattering experiments,” Appl. Opt. 30, 4103–4112 (1991).
[CrossRef] [PubMed]

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Light scattering from one-dimensional surfaces with an even profile,” in Optical Space Communication, G. Otrio, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1131, 18–29 (1990).

Sant, A. J.

A. A. Maradudin, J. Q. Lu, T. Michel, Z.-H. Gu, J. C. Dainty, A. J. Sant, E. R. Méndez, M. Nieto-Vesperinas, “Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films,” Waves Random Med. 1, S129–S141 (1991).
[CrossRef]

M.-J. Kim, J. C. Dainty, A. T. Friberg, A. J. Sant, “Experimental study of enhanced backscattering from one-and two-dimensional random rough surfaces,” J. Opt. Soc. Am. A 7, 569–577 (1990).
[CrossRef]

Soto-Crespo, J. M.

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1989).
[CrossRef]

J. M. Soto-Crespo, M. Nieto-Vesperinas, “Electromagnetic scattering from very rough random surfaces and deep reflection gratings,” J. Opt. Soc. Am. A 6, 367–384 (1989).
[CrossRef]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Light-diffracted intensities from very deep gratings,” Phys. Rev. B 38, 7250 (1988).
[CrossRef]

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 84.

Tran, P.

V. Celli, P. Tran, A. A. Maradudin, J. Lu, T. Michel, Z. H. Gu, “Waves on corrugated surfaces: K-gaps and enhanced backscattering,” in Laser Optics of Condensed Matter, E. Garmire, A. A. Maradudin, K. K. Rebane, eds. (Plenum, New York, 1991), Vol. 2, pp. 315–323.
[CrossRef]

Welford, W. T.

W. T. Welford, “Optical estimation of statistics of surface roughness from light scattering measurements,” Opt. Quantum Electron. 9, 269–287 (1977).
[CrossRef]

Ann. of Phys.

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. of Phys. 203, 255–307 (1990).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

A. R. McGurn, A. A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–281 (1989).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

W. T. Welford, “Optical estimation of statistics of surface roughness from light scattering measurements,” Opt. Quantum Electron. 9, 269–287 (1977).
[CrossRef]

Phys. Rev. B

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Light-diffracted intensities from very deep gratings,” Phys. Rev. B 38, 7250 (1988).
[CrossRef]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1989).
[CrossRef]

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

Waves Random Med.

Z.-H. Gu, A. A. Maradudin, E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Enhanced transmission through randomly rough surfaces,” Waves Random Med. 1, S75–S90 (1991).
[CrossRef]

A. A. Maradudin, J. Q. Lu, T. Michel, Z.-H. Gu, J. C. Dainty, A. J. Sant, E. R. Méndez, M. Nieto-Vesperinas, “Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films,” Waves Random Med. 1, S129–S141 (1991).
[CrossRef]

Other

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, “Light scattering from one-dimensional surfaces with an even profile,” in Optical Space Communication, G. Otrio, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1131, 18–29 (1990).

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), p. 84.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 82.

A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of P-polarized light from a large amplitude random metallic grating,” in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North Holland, Amsterdam, 1990), pp. 157–174.

V. Celli, P. Tran, A. A. Maradudin, J. Lu, T. Michel, Z. H. Gu, “Waves on corrugated surfaces: K-gaps and enhanced backscattering,” in Laser Optics of Condensed Matter, E. Garmire, A. A. Maradudin, K. K. Rebane, eds. (Plenum, New York, 1991), Vol. 2, pp. 315–323.
[CrossRef]

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Fig. 1
Fig. 1

Measured surface profile of the fabricated surface. The centers of symmetry are indicated by the dotted lines.

Fig. 2
Fig. 2

Schematic diagram of the experimental arrangement.

Fig. 3
Fig. 3

Schematic diagram showing the scattering geometry and the notation employed in the transmission case. The two incident directions and the scattering one are indicated, respectively, by the angles θ1, θ2, and θt. The angles are taken as positive in the sense indicated by the arrows.

Fig. 4
Fig. 4

Schematic diagram showing the scattering geometry and the notation employed in the reflection case. The two incident directions and the scattering one are indicated respectively by the angles θ1, θ2, and θr. The angles are taken as positive in the sense indicated by the arrows.

Fig. 5
Fig. 5

Measurements of the transmitted intensity as a function of the angle of scattering θt for the case of angles of incidence θ1 = −1° and θ2 = 5°.

Fig. 6
Fig. 6

Measurements of the transmitted intensity as a function of the angle of scattering θt for the case of angles of incidence θ1 = 15° and θ2 = 21°.

Fig. 7
Fig. 7

Measurements of the reflected intensity as a function of the angle of scattering θr for the caseof angles of incidence θ1 = 20° and θ2 = 26°.

Fig. 8
Fig. 8

Calculated mean intensity in transmission as a function of the angle of scattering θt for the case of angles of incidence θ1 = −1° and θ2 = 5°. For the calculations we employed a = 8 μm, σ = 1.4 μm, λ = 0.6328 μm, and n′ = 1.64. The two beams were in phase at the center of symmetry.

Fig. 9
Fig. 9

Same as Fig. 8 but for angles of incidence θ1 = 15° and θ2 = 21°.

Fig. 10
Fig. 10

Calculated mean intensity in reflection as a function of the angle of scattering θr for the case of angles of incidence θ1 = 20° and θ2 = 26°. For the calculations we employed a = 8 μm, σ = 1.4 μm, and λ = 0.6328 μm. (a) α = 0, (b) expanded view of (a), (c) α = π/2, (d) α = π.

Fig. 11
Fig. 11

(a) The contribution to the mean differential reflection coefficient from the incoherent component of the scattered light as a function of the scattering angle θr when two beams of p-polarized light are incident on a perfectly conducting, one-dimensional, random surface of even symmetry, with θ1 = 20° and θ2 = 30°. At the wavelength employed in the experiments (λ = 0.6328 μm) the roughness of the random surface is characterized by σ = 2.0 μm, a = 2.0 μm, while L = 25.6 μm, L/g = 4.6875, N = 300, and Np = 1000. (b) The single-scattering contribution to the 〈∂Rp/∂θrincoh presented in (a). (c) The pure double-scattering contribution to the 〈∂Rp/∂θrincoh presented in (a).

Fig. 12
Fig. 12

(a) Contribution to the mean differential transmission coefficient from the incoherent component of the transmitted light, as a function of the angle of transmission θt, when two beams of p-polarized light are incident on a transparent dielectric film whose illuminated surface is a one-dimensional, random surface of even symmetry and whose back surface is planar. The angles of incidence are θ1 = 15° and θ2 = 21°. λ = 0.6328 μm, w = 6.18 μm, and n′ = 1.64. The roughness of the random surface is characterized by or σ = 0.35 μm, a = 2.0 μm, while d = 5 μm, L = 25.6 μm, N = 300, and Np = 1500. The phase angle α defined in Eq. (20) is α = 0 rad. (b) Results from the analysis based on the thin-phase screen model. The parameters are the same as for (a).

Fig. 13
Fig. 13

(a) Same as Fig. 12(a), except that α = π/2 rad. (b) Same as Fig. 12(b), except that α = π/2 rad.

Fig. 14
Fig. 14

(a) Same as Fig. 12(a), except that α = π rad. (b) Same as Fig. 12(b), except that α = π rad.

Fig. 15
Fig. 15

Change in the reflected optical path length after a vertical displacement of the scatterer.

Fig. 16
Fig. 16

Change in the transmitted optical path length after a vertical displacement of the scatterer.

Equations (27)

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C ( τ ) = 3 10 a 2 τ 2 [ 1 - sinc ( 2 5 π τ a ) ] ,
A ( θ s ) = i K 1 λ R cos θ s - L / 2 + L / 2 A inc ( x 1 ) × exp [ i ϕ ( x 1 ) ] exp ( i k x 1 sin θ s ) d x 1 ,
ϕ ( x 1 ) = { k ( cos θ r + cos θ i ) ζ e ( x 1 )             in reflection k [ cos θ i - ( n 2 - sin 2 θ t ) 1 / 2 ζ e ( x 1 )             in transmission ,
ϕ ( x 1 ) = ϕ ( - x 1 ) .
A inc ( x 1 ) = K inc [ a 1 exp ( - i k x 1 sin θ 1 ) + a 2 exp ( - i k x 1 sin θ 2 ) ] ,
A 0 ( θ s , θ i ) = i K 1 K inc a i λ R cos θ s 0 + L / 2 exp [ i ϕ ( x 1 ) ] × exp ( i k x 1 ( sin θ s - sin θ i ) ] d x 1 ,
A 0 ( - θ s , θ i ) = i K 1 K inc a i λ R cos θ s - L / 2 0 exp [ i ϕ ( x 1 ) ] × exp ( i k x 1 ( sin θ s - sin θ i ) ] d x 1 .
A ( θ s ) = a 1 A 0 ( θ s , θ 1 ) + a 1 A 0 ( - θ s , - θ 1 ) + a 2 A 0 ( θ s , θ 2 ) + a 2 A 0 ( - θ s , - θ 2 ) .
I ( θ s ) = 2 a 1 2 I 0 ( θ s , θ 1 ) × { 1 + Re [ γ ( θ s , θ 1 ; - θ s , - θ 1 ) ] } + 2 a 2 2 I 0 ( θ s , θ 2 ) × { 1 + Re [ γ ( θ s , θ 2 ; - θ s , - θ 2 ) ] } + 4 a 1 a 2 [ I 0 ( θ s , θ 1 ) I 0 ( θ s , θ 2 ) ] 1 / 2 × cos α × { Re [ γ ( θ s , θ 1 ; θ s , θ 2 ) ] + Re [ γ ( θ s , θ 1 ; - θ s , - θ 2 ) ] } ,
γ ( θ s , θ i ; θ s , θ i ) = A 0 ( θ s , θ i ) A 0 * ( θ s , θ i ) [ I 0 ( θ s , θ i ) I 0 ( θ s , θ i ) ] 1 / 2 .
Re [ γ ( θ s , θ i ; θ s , θ i ) ] = sinc [ L λ ( sin θ s - sin θ s - sin θ i + sin θ i ) ] .
I ( θ s ) = 2 a 1 2 I 0 ( θ s , θ 1 ) × { 1 + sinc [ 2 L λ ( sin θ s - sin θ 1 ) ] } + 2 a 2 2 I 0 ( θ s , θ 2 ) × { 1 + sinc [ 2 L λ ( sin θ s - sin θ 2 ) ] } + 4 a 1 a 2 [ I 0 ( θ s , θ 1 ) I 0 ( θ s , θ 2 ) ] 1 / 2 1 2 cos α × sinc [ 2 L λ ( sin θ s - sin θ 1 + sin θ 2 2 ) ] .
θ s = sin - 1 ( sin θ 1 + sin θ 2 2 ) .
I 0 ( θ s , θ i ) = K 0 L 2 λ 2 R 2 a i 2 ( π a L ) cos 2 θ s σ ϕ × exp [ - a 2 k 2 ( sin θ s - sin θ i ) 2 4 σ ϕ 2 ] ,
ζ ( x 1 ) ζ ( x 1 ) = σ 2 [ 1 - ( x 1 - x 1 ) 2 a 2 + ] ,
H ( X ; t ) = [ 0 , H 2 ( x 1 , x 3 ω ) , 0 ] exp ( - i ω t ) .
ζ ( x 1 ) = 0 ,
ζ ( x 1 ) ζ ( x 1 ) = σ 2 exp [ - ( x 1 - x 1 ) 2 / a 2 ] ,
ζ 2 ( x 1 ) = σ 2 ,
ζ e ( x 1 ) = ½ [ ζ ( x 1 ) + ζ ( - x 1 ) ] .
H 2 > ( x 1 , x 3 ω ) inc = F ( 1 ) ( x 1 , x 3 ω ) + F ( 2 ) ( x 1 , x 3 ω ) ,
F ( i ) ( x 1 , x 3 ω ) = exp { i ω c ( x 1 sin θ i - x 3 cos θ i ) × [ 1 + W i ( x 1 , x 3 ) ] } × exp [ - ( x 1 cos θ i + x 3 sin θ i ) 2 w i 2 ] ,
W i ( x 1 , x 3 ) = c 2 ω 2 w i 2 [ 2 w i 2 ( x 1 cos θ i + x 3 sin θ i ) 2 - 1 ] .
H 2 > ( x 1 , x 3 ω ) inc = F ( 1 ) ( x 1 , x 3 ω ) + exp ( i α ) F ( 2 ) ( x 1 , x 3 ω ) ,
( ϕ 2 - ϕ 1 ) = k ( cos θ i + cos θ r ) ζ .
( ϕ 2 - ϕ 1 ) = k ( n cos θ i - n cos θ t ) ζ .
cos θ t = [ 1 - ( n n ) 2 sin 2 θ t ] 1 / 2 .

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